A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
From inside the book
Results 1-5 of 61
Page xxiii
... POLAR COORDINATES . SECTION 1. - Extension of the modes of interpretation , and on the equations to some polar curves . 251. Interpretation of r and when affected with negative signs 411 262-265 . Equations to the Spiral of Archimedes ...
... POLAR COORDINATES . SECTION 1. - Extension of the modes of interpretation , and on the equations to some polar curves . 251. Interpretation of r and when affected with negative signs 411 262-265 . Equations to the Spiral of Archimedes ...
Page xxiv
... polar curves . 298-300 . Length of radius of curvature 456 301. On the chord of curvature , its definition and value 302. Examples in illustration 458 458 SECTION 4. - Evolutes of polar curves . 303. Method of finding the equation to ...
... polar curves . 298-300 . Length of radius of curvature 456 301. On the chord of curvature , its definition and value 302. Examples in illustration 458 458 SECTION 4. - Evolutes of polar curves . 303. Method of finding the equation to ...
Page xxv
... polar envelope 480 319. The degree of the first polar envelope 481 320. Reciprocal curves 483 321. Properties of reciprocal polars 484 SECTION 4. - On caustics . 322. On the formation of caustics 486 323 , 324. Caustic by reflexion of ...
... polar envelope 480 319. The degree of the first polar envelope 481 320. Reciprocal curves 483 321. Properties of reciprocal polars 484 SECTION 4. - On caustics . 322. On the formation of caustics 486 323 , 324. Caustic by reflexion of ...
Page xxvii
... polar surface 555 385. Equation to the polar surface 556 386 , 387. The polar line and locus of polar lines 557 388. The osculating sphere 557 389. Evolutes of non - plane curves 559 390 , 391. Geometrical illustrations 561 392. Complex ...
... polar surface 555 385. Equation to the polar surface 556 386 , 387. The polar line and locus of polar lines 557 388. The osculating sphere 557 389. Evolutes of non - plane curves 559 390 , 391. Geometrical illustrations 561 392. Complex ...
Page 312
... polar coordinates , the equa- tion is r = 2a sin 0 tan 0 . 195. ] The Witch of Agnesi . Fig . 35 . ( 13 ) DEF . In the ordinate MQ of a circle a point p is taken , so that MP : MQ OA : Oм ; the locus of the point P is the Witch of ...
... polar coordinates , the equa- tion is r = 2a sin 0 tan 0 . 195. ] The Witch of Agnesi . Fig . 35 . ( 13 ) DEF . In the ordinate MQ of a circle a point p is taken , so that MP : MQ OA : Oм ; the locus of the point P is the Witch of ...
Contents
1 | |
2 | |
3 | |
4 | |
5 | |
6 | |
7 | |
8 | |
350 | |
356 | |
363 | |
370 | |
377 | |
384 | |
393 | |
411 | |
22 | |
29 | |
30 | |
32 | |
34 | |
37 | |
71 | |
85 | |
97 | |
115 | |
121 | |
128 | |
137 | |
143 | |
149 | |
155 | |
156 | |
162 | |
169 | |
180 | |
187 | |
210 | |
211 | |
224 | |
230 | |
232 | |
236 | |
243 | |
250 | |
257 | |
258 | |
259 | |
260 | |
262 | |
263 | |
264 | |
266 | |
270 | |
271 | |
273 | |
274 | |
279 | |
280 | |
282 | |
284 | |
285 | |
287 | |
288 | |
291 | |
292 | |
293 | |
295 | |
297 | |
303 | |
311 | |
320 | |
326 | |
330 | |
334 | |
336 | |
344 | |
417 | |
423 | |
433 | |
439 | |
447 | |
454 | |
461 | |
468 | |
475 | |
481 | |
491 | |
493 | |
494 | |
495 | |
496 | |
497 | |
498 | |
500 | |
501 | |
502 | |
503 | |
504 | |
506 | |
509 | |
511 | |
513 | |
514 | |
516 | |
518 | |
520 | |
521 | |
534 | |
547 | |
553 | |
559 | |
561 | |
565 | |
574 | |
575 | |
576 | |
579 | |
582 | |
584 | |
586 | |
589 | |
591 | |
593 | |
594 | |
597 | |
598 | |
600 | |
601 | |
603 | |
604 | |
606 | |
607 | |
608 | |
609 | |
610 | |
Other editions - View all
Common terms and phrases
a₁ algebraical angles asymptote axis b₁ becomes Calculus change of sign changes sign circle coefficients constants critical values curve cycloid d2F d2F d²x d²y d2y dx2 d³u d³y determine differential equation dimensions dr dr dr dy drawn dx dx dx dy dx² dy dx dy dy dy dz dy² elimination epitrochoid equa equal equicrescent expression F(xo F(xo+h factors finite quantity function geometrical Hence homogeneous function hyperbola increases infinite infinitesimal Infinitesimal Calculus infinity maxima and minima maximum or minimum minimum value negative nth degree origin partial derived-functions pass plane of reference positive radius real roots right-hand member roots of f(x shewn Similarly singular value straight line Sturm's Theorem substituting symbols tangent Theorem tion u₁ vanish variables variations whence zero